Display device

ABSTRACT

According to one embodiment, a display device includes a display panel, a first light guide, and a second light guide. In the first light guide, a first main surface includes a first plane and first grooves between the first plane and a first side surface, a second main surface includes second grooves orthogonal to the first grooves, and a second plane between the second grooves and the first side surface. In the second light guide, a third main surface includes a third plane and third grooves located between the third plane and a fourth side surface, a fourth main surface includes fourth grooves orthogonal to the third grooves, and a fourth plane located between the fourth grooves and the fourth side surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/970,578, filed Oct. 21, 2022, which is based upon and claims thebenefit of priority from Japanese Patent Application No. 2021-173221,filed Oct. 22, 2021, the entire contents of each are incorporated hereinby reference.

FIELD

Embodiments described herein relate generally to a display device.

BACKGROUND

For example, a display device such as a liquid crystal display devicecomprises a display panel equipped with pixels and an illuminationdevice that illuminates the display panel. The illumination devicecomprises a light source that emits light and a light guide to which thelight from the light source is applied. The light from the light sourceis made incident on a side surface of the light guide, propagates theinside of the light guide, and is emitted from an emission surfacecorresponding to one main surface of the light guide.

For example, a backlight device with two light guides stacked on eachother is known. In such a case where two light guides are stacked, ifnon-uniformity in luminance occurs in the illumination light emittedfrom the emission surface, the display quality of the image displayed onthe display panel may be degraded.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exploded perspective view showing a configuration exampleof a display device of an embodiment.

FIG. 2 is a perspective view showing the first light guides LG1 and thesecond light guides LG2 shown in FIG. 1 .

FIG. 3 is a cross-sectional view showing the illumination device ILshown in FIG. 1 .

FIG. 4A is a cross-sectional view showing an example of the first lightguide LG1 shown in FIG. 2 .

FIG. 4B is a cross-sectional view showing another example of the firstlight guide LG1 shown in FIG. 2 .

FIG. 5 is a cross-sectional view showing the display device DSP shown inFIG. 1 .

FIG. 6 is a cross-sectional view showing Example 1 of the illuminationdevice IL shown in FIG. 1 .

FIG. 7 is a cross-sectional view showing Example 2 of the illuminationdevice IL shown in FIG. 1 .

FIG. 8 is a cross-sectional view showing Example 3 of the illuminationdevice IL shown in FIG. 1 .

FIG. 9A is a view illustrating Evaluation Result 1.

FIG. 9B is a view illustrating Evaluation Result 1.

FIG. 10A is a view illustrating Evaluation Result 2.

FIG. 10B is a view illustrating Evaluation Result 2.

FIG. 11A is a view illustrating Evaluation Result 3.

FIG. 11B is a view illustrating Evaluation Result 3.

FIG. 11C is a view illustrating Evaluation Result 3.

FIG. 12A is a view illustrating Evaluation Result 4.

FIG. 12B is a view illustrating Evaluation Result 4.

FIG. 13A is a view illustrating Evaluation Result 5.

FIG. 13B is a view illustrating Evaluation Result 5.

FIG. 14 is a graph showing a relationship between the contact angle θ ofthe protruding portions forming the first groove G1 and the length L11of the first groove G1.

FIG. 15 is a graph illustrating a relationship between the value of thecontact angle θ and the value of the length L11.

FIG. 16 is a view illustrating a relationship between a thickness T ofthe first light guide LG1 and a length L11 of the first groove G1.

FIG. 17 is a view illustrating a relationship between the angle ofincidence α and the length L11 of the first groove G1.

FIG. 18 is a cross-sectional view showing a modified example of theembodiment.

DETAILED DESCRIPTION

In general, according to one embodiment, a display device includes: adisplay panel configured to display an image; a first light guide havinga first main surface opposed to the display panel, a second main surfaceon a side opposite to the first main surface, a first side surface, anda second side surface on a side opposite to the first side surface; asecond light guide having a third main surface opposed to the secondmain surface, a fourth main surface on a side opposite to the third mainsurface, a third side surface close to the first side surface, and afourth side surface located on a side opposite to the third side surfaceand close to the second side surface; a plurality of first light sourcesopposed to the first side surface; and a plurality of second lightsources opposed to the fourth side surface. The first main surfaceincludes a first plane and a plurality of first grooves located betweenthe first plane and the first side surface. The second main surfaceincludes a plurality of second grooves opposed to the first plane andorthogonal to the first grooves, and a second plane located between thesecond grooves and the first side surface. The third main surfaceincludes a third plane and a plurality of third grooves located betweenthe third plane and the fourth side surface and parallel to the firstgrooves. The fourth main surface includes a plurality of fourth groovesopposed to the third plane and orthogonal to the third grooves, and afourth plane located between the fourth grooves and the fourth sidesurface.

One of embodiments will be described hereinafter with reference to theaccompanying drawings.

The disclosure is merely an example, and proper changes in keeping withthe spirit of the invention, which are easily conceivable by a person ofordinary skill in the art, come within the scope of the invention as amatter of course. In addition, in some casings, in order to make thedescription clearer, the widths, thicknesses, shapes and the like, ofthe respective parts are illustrated schematically in the drawings,rather than as an accurate representation of what is implemented.However, such schematic illustration is merely exemplary, and in no wayrestricts the interpretation of the invention. In addition, in thespecification and drawings, the structural elements, which havefunctions identical or similar to the functions described in connectionwith preceding drawings, are denoted by like reference numbers, and anoverlapping detailed description thereof is omitted unless otherwisenecessary.

In the embodiment, a transmissive liquid crystal display device isdisclosed as an example of a display device DSP. In addition, anillumination device applicable to a backlight device of a transmissiveliquid crystal display device is disclosed as an example of anillumination device IL. The main configuration disclosed in theembodiment is applicable to various display devices such as a reflectiveliquid crystal display device, an electronic paper display device withelectrophoretic elements and the like, a display device utilizingmicro-electromechanical systems (MEMS), and a display device employingelectrochromism. In addition, the main configuration disclosed in theembodiment is also applicable to illumination devices used forapplications other than backlight devices.

In the figures, an X-axis, a Y-axis and a Z-axis orthogonal to eachother are described to facilitate understanding as needed. A directionalong the X-axis is referred to as an X-direction or a first direction,a direction along the Y-axis is referred to as a Y-direction or a seconddirection, and a direction along the Z-axis is referred to as aZ-direction or a third direction. A plane defined by the X-axis and theY-axis is referred to as an X-Y plane and viewing the X-Y plane isreferred to as planar view. The first direction X and the seconddirection Y correspond to the directions parallel to a main surface of asubstrate constituting the display device DSP or a main surface of thelight guide included in the illumination device IL. The third directionZ corresponds to a thickness direction of the display device DSP or athickness direction of the light guide.

FIG. 1 is an exploded perspective view showing a configuration exampleof the display device DSP according to the embodiment.

The display device DSP comprises a display panel PNL configured todisplay images, the illumination substrate IL configured to illuminatethe display panel PNL, an IC chip 1, and a wiring board 2.

The display panel PNL is a liquid crystal panel and comprises a firstsubstrate SUB1, a second substrate SUB2, a polarizer PL1, and apolarizer PL2. The first substrate SUB1 and the second substrate SUB2are opposed to each other in the third direction Z. A liquid crystallayer (not shown) is held between the first substrate SUB1 and thesecond substrate SUB2. The polarizer PL1 is opposed to the firstsubstrate SUB1 in the third direction Z and is bonded to the firstsubstrate SUB1. The polarizer PL2 is opposed to the second substrateSUB2 in the third direction Z and is bonded to the second substrateSUB2.

The display panel PNL includes a display area DA where images aredisplayed. The display panel PNL includes, for example, a plurality ofpixels PX arrayed in a matrix in the display area DA. The polarizers PL1and PL2 overlap the display area DA. Polarization axes of the firstpolarizer PL1 and the second polarizer PL2 are, for example, orthogonalto each other in the X-Y plane.

Each of the IC chip 1 and the wiring board 2 is mounted on the firstsubstrate SUB1. The IC chip 1 may be mounted on the wiring board 2. Thewiring board 2 is, for example, a flexible printed circuit board thatcan be bent. The IC chip 1 and the wiring board 2 function mainly assignal sources that output signals necessary for displaying images tothe display panel PNL.

The illumination device IL comprises a first light guide LG1, a secondlight guide LG2, a plurality of first light sources LS1, a plurality ofsecond light sources LS2, a reflective sheet RS, a prism sheet PS, and adiffusion sheet DS. The reflective sheet RS, the second light guide LG2,the first light guide LG1, the prism sheet PS, and the diffusion sheetDS are arranged in this order in the third direction Z.

The first light guide LG1 and the second light guide LG2 are formed inflat plates along the X-Y plane. For example, the first light guide LG1and the second light guide LG2 are formed in a rectangular shape havinglong sides along the first direction X and short sides along the seconddirection Y, in planar view. Lengths of the long sides of the firstlight guide LG1 and the second light guide LG2 may be the same ordifferent. In addition, lengths of the short sides of the first lightguide LG1 and the second light guide LG2 may be the same or different.In the illustrated example, the lengths of the long sides of the firstlight guide LG1 and the second light guide LG2 are the same and thelengths of the short sides of the first light guide LG1 and the secondlight guide LG2 are also the same.

The first light guide LG1 has a first main surface M1, a second mainsurface M2, a first side surface S1, and a second side surface S2.

The first main surface M1 is opposed to the display panel PNL or theprism sheet PS in the third direction Z. The second main surface M2 islocated on a side opposite to the first main surface M1 in the thirddirection Z. In other words, the first main surface M1 and the secondmain surface M2 are opposed to each other in the third direction Z.

The first side surface S1 is opposed to the plurality of first lightsources LS1 in the first direction X and corresponds to thelight-entering surface. The second side surface S2 is located on a sideopposite to the first side surface S1 in the first direction X. In otherwords, the first side surface S1 and the second side surface S2 areopposed to each other in the first direction X. In addition, each of thefirst side surface S1 and the second side surface S2 is formed along theshort sides of the first light guide LG1 to extend in the seconddirection Y. The first side surface S1 and the second side surface S2are, for example, planes parallel to the Y-Z plane defined by the seconddirection Y and the third direction Z.

The plurality of first light sources LS1 are spaced apart and alignedalong the second direction Y and are configured to emit light toward thefirst side surface S1.

The second light guide LG2 has a third main surface M3, a fourth mainsurface M4, a third side surface S3, and a fourth side surface S4.

The third main surface M3 is opposed to the second main surface M2 inthe third direction Z. The fourth main surface M4 is located on a sideopposite to the third main surface M3 in the third direction Z. In otherwords, the third main surface M3 and the fourth main surface M4 areopposed to each other in the third direction Z.

The third side surface S3 is close to the first side surface S1. Thefourth side surface S4 is close to the second side surface S2 and islocated on a side opposite to the third side surface S3 in the firstdirection X. In other words, the third side surface S3 and the fourthside surface S4 are opposed to each other in the first direction X. Inaddition, the fourth side surface S4 is opposed to the plurality ofsecond light sources LS2 in the first direction X and corresponds to alight-entering surface. Each of the third side surface S3 and the fourthside surface S4 is formed along the short sides of the second lightguide LG2 to extend in the second direction Y. The third side surface S3and the fourth side surface S4 are, for example, planes parallel to theY-Z plane.

The plurality of second light sources LS2 are spaced apart and alignedalong the second direction Y and are configured to emit light toward thefourth side surface S4.

The first light sources LS1 and the second light sources LS2 are, forexample, laser light sources such as semiconductor lasers that isconfigured to emit polarized laser light. The first light sources LS1and the second light sources LS2 are not limited to laser light sourcesbut may be, for example, light emitting diodes.

The first light sources LS1 and the second light sources LS2 maycomprise a plurality of light emitting elements that is configured toemit light of different colors. For example, when each of the firstlight sources LS1 and the second light sources LS2 comprises three lightemitting elements that emit red, green, and blue light, the light sourcecan obtain light of a mixture of the colors (for example, white color).

FIG. 2 is a perspective view showing the first light guides LG1 and thesecond light guides LG2 shown in FIG. 1 . In the figure, the first lightsources LS1 and the second light sources LS2 are represented by dottedlines, and the display panel PNL is represented by one-dot chain lines.

The first main surface M1 has a first plane F1 intersecting the secondside surface S2, a plurality of first grooves G1 located between thefirst plane F1 and the first side surface S1, and a fifth plane F5located between the first grooves G1 and the first side surface S1 andintersecting the first side surface S1. The first plane F1 and the fifthplane F5 are flat planes parallel to the X-Y plane. The plurality offirst grooves G1 are located between the first plane F1 and the fifthplane F5 in the first direction X. The plurality of first grooves G1extend in the first direction X and are arranged in the second directionY.

The second main surface M2 has a plurality of second grooves G2 close tothe second side surface S2, and a second plane F2 located between thesecond grooves G2 and the first side surface S1 and intersecting thefirst side surface S1. The second plane F2 is a flat plane parallel tothe X-Y plane. The plurality of second grooves G2 extend in the seconddirection Y and are arranged in the first direction X. In other words,each of the second grooves G2 is orthogonal to the first grooves G1 inplanar view.

The third main surface M3 includes a third plane F3 intersecting thethird side surface S3, a plurality of third grooves G3 located betweenthe third plane F3 and the fourth side surface S4, and a sixth plane F6located between the third grooves G3 and the fourth side surface S4 andintersecting the fourth side surface S4. The third plane F3 and thesixth plane F6 are flat planes parallel to the X-Y plane. The pluralityof third grooves G3 are located between the third plane F3 and the sixthplane F6 in the first direction X. The plurality of third grooves G3extend in the first direction X and are arranged in the second directionY. In other words, the direction of extension of the third grooves G3 isparallel to the direction of extension of the first grooves G1.

The fourth main surface M4 has a plurality of fourth grooves G4 close tothe third side surface S3, and a fourth plane F4 located between thefourth grooves G4 and the fourth side surface S4 and intersecting thefourth side surface S4. The fourth plane F4 is a flat plane parallel tothe X-Y plane. The plurality of fourth grooves G4 extend in the seconddirection Y and are arranged in the first direction X. In other words,each of the fourth grooves G4 is orthogonal to the third grooves G3 inplanar view.

An optical path OP1 of a principal ray with the highest intensity, ofthe light emitted from the first light sources LS1, is parallel to thefirst direction X in planar view. In other words, on the first lightguide LG1, the direction of extension of each of the first grooves G1 isparallel to the optical path OP1, and the direction of extension of eachof the second grooves G2 is perpendicular to the optical path OP1.

An optical path OP2 of a principal ray with the highest intensity, ofthe light emitted from the second light sources LS2, is parallel to thefirst direction X in planar view. In other words, on the second lightguide LG2, the direction of extension of each of the third grooves G3 isparallel to the optical path OP2, and the direction of extension of eachof the fourth grooves G4 is orthogonal to the optical path OP2.

FIG. 3 is a cross-sectional view showing the illumination device ILshown in FIG. 1 . A cross-sectional view of the first light guide LG1and the second light guide LG2 along the X-Z plane defined by the firstdirection X and the third direction Z is shown in FIG. 3 .

The illumination device IL includes a first area A1 and a second area A2that are arranged in the first direction X. A case where the first lightguide LG1 and the second light guide LG2 have the same length along thefirst direction X, the first side surface S1 is located directly abovethe third side surface S3, and the second side surface S2 is locateddirectly above the fourth side surface S4 will be described.

A length L1 of the first area A1 along the first direction X is equal toa length L2 of the second area A2 along the first direction X. Aboundary B between the first area A1 and the second area A2 is locatedat a middle point between the first side surface S1 and the second sidesurface S2, and is also located at a middle point between the third sidesurface S3 and the fourth side surface S4.

On the first light guide LG1, the second grooves G2 are formed in thefirst area A1 from the second side surface S2 to the boundary B and arealso formed in the second area A2. In other words, the length L12 alongthe first direction X of the area where the second grooves G2 are formedis longer than the length L1 of the first area A1.

The second groove G2 is formed between two protruding portions P2adjacent to each other in the first direction X. In other words, aplurality of second grooves G2 are formed by a plurality of protrudingportions P2. Each of the protruding portions P2 is a prism extending inthe second direction Y and has a triangular cross-sectional shape.

The first plane F1 is located in the first area A1 and is opposed to thesecond grooves G2 in the third direction Z. Such a first plane F1corresponds to an emission surface on which the light propagating insidethe first light guide LG1 is emitted to the outside.

The second plane F2 and the fifth plane F5 are located in the secondarea A2. The fifth plane F5 is opposed to the second plane F2 in thethird direction Z. In the example illustrated, the first grooves G1 arelocated in the second area A2 and opposed to the second plane F2. Atleast part of the first grooves G1 may be opposed to the second groovesG2.

On the second light guide LG2, the fourth grooves G4 are formed in thesecond area A2 from the third side surface S3 to the boundary B and arealso formed in the first area A1. In other words, a length L14 along thefirst direction X of the area where the fourth grooves G4 are formed islonger than the length L2 of the second area A2.

The fourth groove G4 is formed between two protruding portions P4adjacent to each other in the first direction X. In other words, theplurality of fourth grooves G4 are formed by the plurality of protrudingportions P4. Each of the protruding portions P4 is a prism extending inthe second direction Y and has a triangular cross-sectional shape.

The third plane F3 is located in the second area A2 and opposed to thefourth grooves G4 in the third direction Z. Such a third plane F3corresponds to an emission surface on which the light propagating insidethe second light guide LG2 is emitted to the outside.

The fourth plane F4 and the sixth plane F6 are located in the first areaA1. The sixth plane F6 is opposed to the fourth plane F4 in the thirddirection Z. In the example illustrated, the third grooves G3 arelocated in the first area A1 and opposed to the fourth plane F4. Atleast part of the third grooves G3 may be opposed to the fourth groovesG4.

FIG. 4A is a cross-sectional view showing the first light guide LG1shown in FIG. 2 . A cross-sectional view of the first light guide LG1including the first grooves G1 along the Y-Z plane defined by the seconddirection Y and the third direction Z is shown in FIG. 4A.

The first groove G1 is formed between two protruding portions P1adjacent to each other in the second direction Y. In other words, theplurality of first grooves G1 are formed by the plurality of protrudingportions P1. Each of the protruding portions P1 extends in the firstdirection X and has a curved surface. The curved surface is acylindrical surface, but the cross-section is not limited to an arc.

The protruding portion P1 has a width W in the second direction Y. Inaddition, the adjacent protruding portion P1 is arranged at a pitch PT.For example, the width W is substantially equal to the pitch PT.

When the angle formed between a tangent of the protruding portion P1 andthe X-Y plane is defined as a contact angle θ of the protruding portionP1, the contact angle θ is, for example, in a range from 2° to 10°.

The first groove G1 has been described with reference to FIG. 4A, butthe third groove G3 is also formed in the same manner as the firstgroove G1 and its illustration and detailed explanation are omitted. Inthe example shown in FIG. 4A, the first groove G1 has a plane parallelto the second plane F2 but may not have the parallel plane. In otherwords, as shown in FIG. 4B, adjacent protruding portions P1 may becontinuously formed.

FIG. 5 is a cross-sectional view showing the display device DSP shown inFIG. 1 .

In the display panel PNL, the liquid crystal layer LC and the sealant SEare located between the first substrate SUB1 and the second substrateSUB2. The sealant SE bonds the first substrate SUB1 and the secondsubstrate SUB2 and seals the liquid crystal layer LC between the firstsubstrate SUB1 and the second substrate SUB2.

In the illumination device IL, the reflective sheet RS comprises afunction of reflecting the light that leaks from the second light guideLG2 toward the second light guide LG2. The prism sheet PS comprises afunction of collecting light emitted from the first main surface M1 ofthe first light guide LG1. A plurality of prism sheets PS may bearranged between the first light guide LG1 and the diffusion sheet DS.The diffusion sheet DS comprises a function of diffusing the light madeincident on the diffusion sheet DS to uniform the luminance of thelight.

The light L1 emitted from the first light source LS1 is refracted on thefirst side surface S1 and is made incident on the first light guide LG1.The light L1 made incident on the first light guide LG1 travels towardthe first main surface M1 and is reflected at an interface between thefirst light guide LG1 and an air layer. The reflected light L1 travelstoward the second main surface M2 and is reflected at the interfacebetween the first light guide LG1 and the air layer. Thus, in the secondarea A2, the light L1 travels through the inside of the first lightguide LG1 while being repeatedly reflected on the first main surface M1and the second main surface M2. In addition, the light L1 travelingtoward the first groove G1 is diffused moderately in a directionorthogonal to the direction of travel of the light L1 when reflected bythe protruding portion P1 of the first groove G1.

The light L1 traveling toward the second groove G2, of the light L1traveling inside the first light guide LG1 toward the first area A1 isreflected by the protruding portion (prism) P2 of the second groove G2and is emitted from the first main surface M1 without meeting the totalreflection conditions of the first main surface M1. The light mainlyemitted from the first main surface M1 of the first area A1 illuminatesthe display panel PNL through the prism sheet PS and the diffusion sheetDS.

Similarly, the light L2 emitted from the second light source LS2 isrefracted on the fourth side surface S4 and is made incident on thesecond light guide LG2. In the first area A1, the light L2 travelsthrough the inside of the second light guide LG2 while being repeatedlyreflected on the third main surface M3 and the fourth main surface M4.In addition, the light L2 traveling toward the third grooves G3 isdiffused moderately in a direction orthogonal to the direction of travelof the light L2 when reflected by the protruding portion of the thirdgrooves G3. Furthermore, the light L2 traveling toward the fourthgrooves G4, of the light L2 traveling inside the second light guide LG2toward the second area A2 is reflected by the protruding portion (prism)of the fourth grooves G4 and is emitted from the third main surface M3without meeting the total reflection conditions of the third mainsurface M3. The light mainly emitted from the third main surface M3 inthe second area A2 illuminates the display panel PNL through the prismsheet PS and the diffusion sheet DS.

In general, the light from a plurality of light sources arranged andspaced apart at intervals travels inside the light guide whilediffusing, but these light beams are not sufficiently mixed in thevicinity of the light sources. For this reason, in a display deviceusing such light as the illumination light, there is a risk that linearnon-uniformity in luminance caused by differences in luminance may bevisibly recognized when the display area is viewed in planar view. Inparticular, laser light has high luminance, but is highly directionaland has a small diffusivity in the direction orthogonal to the directionof travel of laser light.

According to the embodiment, in the first light guide LG1, the light L1is diffused in a direction orthogonal to the direction of travel sincethe first groove G1 extending in the direction of travel of the light L1is provided. For this reason, the light L1 that has reached the firstarea A1 mixes with each other and can produce illumination light withsuppressed non-uniformity in luminance.

Similarly, in the second light guide LG2, the light L2 is diffused in adirection orthogonal to the direction of travel since the third groovesG3 extending in the direction of travel of the light L2 is provided. Forthis reason, the light L2 that has reached the second area A2 mixes witheach other and can produce illumination light with suppressednon-uniformity in luminance.

Therefore, degradation in display quality caused by the non-uniformityin luminance of the illumination light can be suppressed.

FIG. 6 is a cross-sectional view showing Example 1 of the illuminationdevice IL shown in FIG. 1 .

First, the first light guide LG1 will be described.

The first groove G1, the fifth plane F5, and the second plane F2 arelocated in the second area A2. The first groove G1 and the fifth planeF5 are opposed to the second plane F2 in the third direction Z. Thefirst plane F1 and the second groove G2 are located in the first area A1and are also located in a part of the second area A2 beyond the boundaryB. The first plane F1 is opposed to the second groove G2 in the thirddirection Z.

The first groove G1 is not opposed to the second groove G2 in the thirddirection Z. In addition, in the example shown in FIG. 6 , almost no gapexists between the first groove G1 and the second groove G2 in planarview. In other words, the first plane F1 and the second plane F2 are notopposed to each other in the third direction Z. In other words, aboundary B1 between the first groove G1 and the first plane F1 overlapsa boundary B2 between the second groove G2 and the second plane F2. Aboundary B5 between the first groove G1 and the fifth plane F5 overlapsthe second plane F2.

In addition, the length L11 of the first groove G1 along the firstdirection X is smaller than the length L15 of the fifth plane F5 alongthe first direction X. For example, in the first light guide LG1 inwhich a diagonal length in planar view is 127 mm (equivalent to 5inches), the length L11 is 6.4 mm and the length L15 is 37 mm. When thelength along the third direction Z between the second plane F2 and thefifth plane F5 is referred to as a thickness T of the first light guideLG1, the thickness T is 1 mm. A contact angle θ of the protrudingportion P1 that forms the first groove G1 is 5.6°.

Next, the second light guide LG2 will be described. The second lightguide LG2 has the same shape as the first light guide LG1. In otherwords, the first light guide LG1 and the second light guide LG2 have across-sectional shape that has line symmetry about the boundary B in thecross-sectional view of the X-Z plane.

The third groove G3, the sixth plane F6, and the fourth plane F4 arelocated in the first area A1. The third groove G3 and the sixth plane F6are opposed to the fourth plane F4 in the third direction Z. The thirdplane F3 and the fourth grooves G4 are located in the second area A2 andare also located in a part of the first area A1 beyond the boundary B.The third plane F3 is opposed to the fourth grooves G4 in the thirddirection Z.

The third groove G3 is not opposed to the fourth groove G4 in the thirddirection Z. In addition, in the example shown in FIG. 6 , almost no gapexists between the third grooves G3 and the fourth grooves G4 in planarview. In other words, the third plane F3 and the fourth plane F4 are notopposed to each other in the third direction Z. In other words, aboundary B3 between the third groove G3 and the third plane F3 overlapsa boundary B4 between the fourth groove G4 and the fourth plane F4. Aboundary B6 between the third grooves G3 and the sixth plane F6 overlapsthe fourth plane F4.

In addition, the length L13 of the third groove G3 along the firstdirection X is smaller than the length L16 of the sixth plane F6 alongthe first direction X. In Example 2 and Example 3 described below, theillumination device IL in which at least part of the plurality of firstgrooves G1 are opposed to the plurality of second grooves G2 and atleast part of the plurality of third grooves G3 are opposed to theplurality of fourth grooves G4 will be described.

FIG. 7 is a cross-sectional view showing Example 2 of the illuminationdevice IL shown in FIG. 1 .

In the first light guide LG1, the fifth plane F5 located between thefirst groove G1 and the first side surface S1 is opposed to the secondplane F2 in the third direction Z. The fifth plane F5 and the secondplane F2 are located in the second area A2. The first plane F1 and thefirst groove G1 are opposed to the second groove G2 in the thirddirection Z. The first groove G1 is not opposed to the second plane F2.In addition, the fifth plane F5 is not opposed to the second groove G2.In other words, the boundary B5 between the first groove G1 and thefifth plane F5 overlaps the boundary B2 between the second groove G2 andthe second plane F2.

In addition, the length L11 of the first groove G1 along the firstdirection X is smaller than the length L15 of the fifth plane F5 alongthe first direction X. For example, in the first light guide LG1 inwhich a diagonal length in planar view is 127 mm (equivalent to 5inches), the length L11 is 6.4 mm and the length L15 is 44 mm.

In the second light guide LG2, the sixth plane F6 located between thethird grooves G3 and the fourth side surface S4 is opposed to the fourthplane F4 in the third direction Z. The sixth plane F6 and the fourthplane F4 are located in the first area A1. The third plane F3 and thethird grooves G3 are opposed to the fourth grooves G4 in the thirddirection Z. The third grooves G3 is not opposed to the fourth plane F4.In addition, the sixth plane F6 is not opposed to the fourth grooves G4.In other words, the boundary B6 between the third groove G3 and thesixth plane F6 overlaps the boundary B4 between the fourth groove G4 andthe fourth plane F4.

In addition, the length L13 of the third groove G3 along the firstdirection X is smaller than the length L16 of the sixth plane F6 alongthe first direction X.

FIG. 8 is a cross-sectional view showing Example 3 of the illuminationdevice IL shown in FIG. 1 .

In the first light guide LG1, the first plane F1 and the first groove G1are opposed to the second groove G2 in the third direction Z. Inaddition, the first groove G1 and the fifth plane F5 are opposed to thesecond plane F2 in the third direction Z. The first plane F1 is notopposed to the second plane F2. In addition, the fifth plane F5 is notopposed to the second groove G2. The boundary B5 between the firstgroove G1 and the fifth plane F5 is opposed to the second plane F2 inthe third direction Z. In addition, the boundary B2 between the secondgroove G2 and the second plane F2 is opposed to the first groove G1 inthe third direction Z.

In the second light guide LG2, the third plane F3 and the third groovesG3 are opposed to the fourth grooves G4 in the third direction Z. Inaddition, the third groove G3 and the sixth plane F6 are opposed to thefourth plane F4 in the third direction Z. The third plane F3 is notopposed to the fourth plane F4. In addition, the sixth plane F6 is notopposed to the fourth grooves G4. The boundary B6 between the thirdgroove G3 and the sixth plane F6 is opposed to the fourth plane F4 inthe third direction Z. In addition, the boundary B4 between the fourthgroove G4 and the fourth plane F4 is opposed to the third groove G3 inthe third direction Z.

Next, the inventors evaluated the first light guide LG1 with differentspecifications of the first groove G1. Results of evaluation will bedescribed below.

FIG. 9A and FIG. 9B are views illustrating Evaluation Result 1.

In the first light guide LG11 shown in FIG. 9A, the first grooves G1have a length L11A along the first direction X. In the first light guideLG12 shown in FIG. 9B, the first grooves G1 have a length L11B along thefirst direction X. The length L11A is greater than the length L11B.

Comparison in optical characteristics between the illumination devicesIL to which the first light guides LG11 and LG12 were respectivelyapplied indicated an evaluation result that the obtained effect wasdifferent depending on the length of the first grooves G1. In otherwords, the longer the first grooves G1 are, the more effective theimprovement of the non-uniformity in luminance is. In contrast, theshorter the first grooves G1 are, the higher the luminance of theillumination light is. In addition, the polarization degree of the lightemitted from the first light sources LS1 is higher as the first groovesG1 are shorter.

FIG. 10A and FIG. 10B are views illustrating Evaluation Result 2.

In a first light guide LG13 shown in FIG. 10A, the first grooves G1 areclose to the first light source LS1 and are separated from the secondgrooves G2 (L15=0 mm). In a first light guide LG14 shown in FIG. 10B,the first grooves G1 are separated from the first light sources LS1 andare close to the second grooves G2. In all the first grooves G1, thelength L11 along the first direction X is equal.

Comparison in optical characteristics between the illumination devicesIL to which the first light guides LG13 and LG14 were appliedrespectively indicates an evaluation result that the effect ofimprovement of the non-uniformity in luminance was different dependingon the position of formation of the first grooves G1. In other words,the non-uniformity in luminance was visually recognized in the area A10overlapping the second grooves G2, in the first light guide LG13, whilethe non-uniformity in luminance was hardly recognized in the area A10overlapping the second grooves G2, in the first light guide LG14. Inother words, the first grooves G1 are desirably separated from the firstlight sources LS1, based on the viewpoint of improving thenon-uniformity in luminance.

FIG. 11A, FIG. 11B and FIG. 11C are views illustrating Evaluation Result3.

In a first light guide LG15 shown in FIG. 11A, the first grooves G1 areopposed to the second grooves G2, and the boundary B2 is located betweenthe boundary B5 and the first light sources LS1. In a first light guideLG16 shown in FIG. 11B, the first grooves G1 are opposed to the secondgrooves G2, and the boundary B2 overlaps the boundary B5. In a firstlight guide LG17 shown in FIG. 11C, the first grooves G1 are not opposedto the second grooves G2, and the boundary B5 is located between theboundary B2 and the first light sources LS1. In all the first groovesG1, the length L11 along the first direction X is equal.

Comparison in optical characteristics between the illumination devicesIL to which the first light guides LG15 to LG17 were appliedrespectively indicates an evaluation result that the effect ofimprovement of the non-uniformity in luminance was different dependingon the position of formation of the first grooves G1. In other words, inthe first light guide LG15, the non-uniformity in luminance was hardlyrecognized visibly in the area A11 from the boundary B5 to the secondside surface S2, of the area overlapping the second grooves G2, and thenon-uniformity in luminance was visibly recognized in the area A12between the boundary B2 and the boundary B5, of the area overlapping thesecond grooves G2. In the first light guides LG16 and LG17, thenon-uniformity in luminance was hardly recognized visibly in the areaA10 overlapping the second grooves G2. In other words, desirably, theboundary B5 overlaps the boundary B2 or is closer to the first lightsources LS1 than the boundary B2, based on the viewpoint of improvingthe non-uniformity in luminance.

FIG. 12A and FIG. 12B are views illustrating Evaluation Result 4.

In a first light guide LG18 shown in FIG. 12A, a part of the firstgrooves G1 are opposed to the second grooves G2. In a first light guideLG19 shown in FIG. 12B, the first grooves G1 are not opposed to thesecond grooves G2. In all the first grooves G1, the length L11 along thefirst direction X is equal.

Comparison in optical characteristics between the illumination devicesIL to which the first light guides LG18 and LG19 were appliedrespectively indicates an evaluation result that the polarization degreewas different depending on the position of formation of the firstgrooves G1. In other words, decrease in polarization degree of the lightemitted from the first light sources LS1 was remarkable in the firstlight guide LG18, and the polarization degree of the light emitted fromthe first light sources LS1 was substantially maintained in the firstlight guide LG19. In other words, desirably, a section where the firstgrooves G1 and the second grooves G2 are opposed to each other is notprovided, based on the viewpoint of suppressing the decrease inpolarization degree.

FIG. 13A and FIG. 13B are views illustrating Evaluation Result 5.

In the first light guide LG1 shown in FIG. 13A, protruding portions P11forming the first groove G1 has a contact angle θ1. In the first lightguide LG1 shown in FIG. 13B, protruding portions P12 forming the firstgroove G1 has a contact angle θ2. The contact angle θ1 is larger thanthe contact angle θ2.

Comparison in optical characteristics between the illumination devicesIL to which the first light guides LG1 were respectively appliedindicated an evaluation result that the obtained effect was differentdepending on the magnitude of the contact angle. In other words, thelarger the contact angle, the higher the improvement effect of thenon-uniformity in luminance. In contrast, the decrease in polarizationdegree of the light emitted from the first light sources LS1 issuppressed as the contact angle is smaller.

The first light guide LG1 has been described in Evaluation Results 1 to5 described above, but it goes without saying that the same evaluationresults as those for the first light guide LG1 can also be obtained forthe second light guide LG2.

FIG. 14 is a graph showing a relationship between the contact angle θ ofthe protruding portions forming the first groove G1 and the length L11of the first groove G1.

In the graph, the horizontal axis indicates the contact angle θ (′), andthe vertical axis indicates the length L11 (mm).

The conditions under which the luminance ratio is the same and thepolarization degree is the same in the illumination devices different incontact angle θ and length L11, are connected by lines, respectively.The luminance ratio is a relative value in a case where the luminance ofthe light emitted from the illumination device under the condition wherethe first groove G1 is not provided is set to 100. The polarizationdegree indicates polarization degree of the linearly polarized lightemitted from the illumination device.

In the graph, L98, L96, L94, and L92 indicate that the luminance ratiosare 98%, 96%, 94%, and 92%, respectively. In the graph, P90, P88, P86,and P84 indicate that the polarization degrees are 90%, 88%, 86%, and84%, respectively.

It was confirmed from the relationships shown in the graph that as thecontact angle θ is smaller and as the length L11 is shorter, a higherluminance ratio can be obtained and higher polarization degree can beobtained.

FIG. 15 is a graph illustrating a relationship between the value of thecontact angle θ and the value of the length L11.

In the graph, the horizontal axis indicates the contact angle θ (°), andthe vertical axis indicates the length L11 (mm).

Presence or absence of the non-uniformity in luminance on seven sampleswas confirmed. A thickness T of each light guide was 1.0 mm, and theangle of incidence α of the light from the light source to the lightguide was 26.5°.

Sample SP1 had the contact angle θ of 1.7° and the length L11 of 1.9 mm.

Sample SP2 had the contact angle θ of 2.1° and the length L11 of 2.3 mm.

Sample SP3 had a contact angle θ of 5.0° and a length L11 of 3.5 mm.

Sample SP4 had the contact angle θ of 4.5° and the length L11 of 5.2 mm.

Sample SP5 had a contact angle θ of 1.7° and a length L11 of 3.0 mm.

Sample SP6 had the contact angle θ of 2.2° and the length L11 of 3.9 mm.

Sample SP7 had the contact angle θ of 4.8° and the length L11 of 3.5 mm.

FIG. 15 also shows a line connected under the condition that thepolarization degree is 88% and a line connected under the condition thatthe polarization degree is 84%, as shown in FIG. 14 . This is an excerptfrom FIG. 14 since the polarization degree is desirably at least 84% ormore, more desirably 88% or more, based on the viewpoint of suppressingthe degradation in display quality. As shown in FIG. 15 , thepolarization degree of all samples SP1 to SP7 was 88% or more, and thereis no problem on the polarization degree. In contrast, non-uniformity inluminance was visibly recognized in the emitted light from theillumination device for samples SP1 and SP5. For the other samples, nonon-uniformity in luminance was visually recognized. In other words, itwas confirmed that a higher luminance ration and a higher polarizationdegree can be obtained as values of the contact angle θ and length L11are smaller and that the non-uniformity in luminance cannot besuppressed when the values of contact angle θ and length L11 are toosmall. It was confirmed from these results that, desirably, based on theviewpoint of suppressing the non-uniformity in luminance, the contactangle θ should be set with reference to 2° and the length L11 should beset with reference to 2 mm, in consideration of the relationship betweenthe thickness T of the light guide and the angle of incidence α, whichwill be described later.

The values of contact angle θ and length L11 described here are notapplied only to the protruding portions forming the first groove G1, butalso to protruding portions forming a third groove G3 and a length L13of the third groove G3.

FIG. 16 is a view illustrating a relationship between a thickness T ofthe first light guide LG1 and a length L11 of the first groove G1.

An upper stage of FIG. 16 shows a first light guide LG1A having athickness T of 1.0 mm and a length L11 of 10 mm.

A middle stage of FIG. 16 shows a first light guide LG1B having athickness T of 2.2 mm and a length L11 of 10 mm.

A lower stage of FIG. 16 shows a first light guide LG1C having athickness T of 2.2 mm and a length L11 of 22 mm.

The angle of incidence α of the light from the first light sources LS1is 26.5° for any of the first light guides.

In the first light guide LG1A of the upper stage, it is shown that thelight traveling inside is reflected three times in the first groove G1.

In the first light guide LG1B of the middle stage, the length L11 is thesame as that of the first light guide LG1A, but the thickness T is 2.2times that of the first light guide LG1A. In the first light guide LG1B,the light traveling inside is reflected twice in the first groove G1. Insuch a first light guide LG1B, since the number of reflections in thefirst groove G1 is smaller than that in the first light guide LG1A, thedegree of diffusion at the first groove G1 is reduced and thenon-uniformity in luminance can be recognized more easily than that inthe first light guide LG1A.

In the first light guide LG1C of the lower stage, the length L11 is 2.2times that of the first light guide LG1A, and the thickness T is 2.2times that of the first light guide LG1A. In the first light guide LG1C,the light traveling inside is reflected three times in the first grooveG1. In other words, in such a first light guide LG1C, since the numberof reflections in the first groove G1 is larger than that in the firstlight guide LG1B, the non-uniformity in luminance can be recognized morehardly than that in the first light guide LG1B.

In short, when the angle of incidence α of the light to the first lightguide LG1 is constant, the length L11 needs be increased as thethickness T is increased, based on the viewpoint of suppressing thenon-uniformity in luminance.

FIG. 17 is a view illustrating a relationship between the angle ofincidence α and the length L11 of the first groove G1.

An upper stage of FIG. 17 shows a first light guide LG1D having an angleof incidence α1 of 17.6° and the length L11 of 10 mm.

A lower stage of FIG. 17 shows a first light guide LG1E having an angleof incidence α2 of 26.5° and the length L11 of 10 mm.

The thickness T is 1.0 mm in both the first light guides.

In a first light guide LG1E of the lower stage, it is shown that thelight traveling inside is reflected three times in the first groove G1.

In a first light guide LG1D of the upper stage, the length L11 is thesame as that of the first light guide LG1E, but the angle of incidenceα1 is smaller than the angle of incidence α2. In the first light guideLG1D, the light traveling inside is reflected twice in the first grooveG1. In such a first light guide LG1D, since the number of reflections inthe first groove G1 is smaller than that in the first light guide LG1E,the degree of diffusion in the first groove G1 is reduced and thenon-uniformity in luminance can be recognized more easily than that inthe first light guide LG1E.

In short, when the thickness T of the first light guide LG1 is madeconstant, the length L11 needs to be increased as the angle of incidenceα is smaller, from the viewpoint of suppressing the non-uniformity inluminance.

The angle of incidence α commonly set in FIG. 16 is the angle at whichlight can be made incident on the light guide LG with the least loss. Inaddition, the thickness T commonly set in FIG. 17 is the thickness ofthe most common light guide.

It was confirmed from the results shown in FIG. 16 and FIG. 17 that theoptimal values of the contact angle θ and the length L11 to suppress thenon-uniformity in luminance are different depending on the thickness Tof the light guide LG and the angle of incidence α of the light on thelight guide LG.

Thus, when a length L11 is referred to as a referential length Lo, thecontact angle θ is referred to as a reference contact angle θo, theangle of incidence to be applied is referred to as δ, and the thicknessof the light guide to be applied is referred to as d, in a case wherethe thickness T of the light guide LG is 1.0 mm and the angle ofincidence α of the light on the light guide LG is 26.5°, the optimalvalue of the length L11 can be obtained from the following equation (1).

$\begin{matrix}{{L11} = {\frac{\tan 26.5{^\circ}}{\tan\delta}L_{0}d}} & (1)\end{matrix}$

In addition, the optimal value of the contact angle θ can be obtainedfrom the following equation (2).

$\begin{matrix}{\theta = \frac{{arc}\sin\left( {\sin 2\theta_{0}\frac{\tan 26.5{^\circ}}{\tan\delta}} \right)}{2}} & (2)\end{matrix}$

When the referential length Lo and the referential contact angle θoshown here are set to be Lo≥2 mm and θo≥2° based on the results shown inFIG. 15 , the non-uniformity in luminance can be suppressed.

FIG. 18 is a cross-sectional view showing a modified example of theembodiment.

The modified example shown in FIG. 18 is different from the exampleshown in FIG. 5 in that that illumination device IL comprises twodiffusion sheets DS1 and DS2. In other words, the diffusion sheet DS1 islocated between the prism sheet PS and the diffusion sheet DS2, and thediffusion sheet DS2 is located between the diffusion sheet DS1 and thepolarizer PL1. An interval between the diffusion sheets DS1 and DS2along the third direction Z is 1 mm or more and, more desirably, 2 mm ormore.

In such a modified example, the effect of improving the non-uniformityin luminance, which is equal to or more than that described above, canbe obtained.

It was confirmed in the above embodiment that when the luminancedistribution is compared in a case where the first plane F1 which is theemission surface is a mirror surface and a case where the first plane F1is a rough surface, for example, in the first light guide LG1, theeffect of improving the non-uniformity in luminance in a case where thefirst plane F1 is a rough surface is higher. For this reason, the firstplane F1 is desirably a rough surface in the first light guide LG1. Incontrast, the second plane F2 desirably has a high reflectivity for thelight L1 traveling in the second area A2 and is desirably a mirrorsurface. For this reason, in the first light guide LG1, the surfaceroughness of the first plane F1 is desirably larger than the surfaceroughness of the second plane F2.

Similarly, in the second light guide LG2, the surface roughness of thethird plane F3 is desirably larger than the surface roughness of thefourth plane F4.

As described above, according to the embodiments, a display device DSPcapable of suppressing deterioration in display quality can be provided.

All of the illumination devices and display devices that can beimplemented by a person of ordinary skill in the art through arbitrarydesign changes to the illumination devices and display devices describedabove as embodiments of the present invention come within the scope ofthe present invention as long as they are in keeping with the spirit ofthe present invention.

Various types of the modified examples are easily conceivable within thecategory of the ideas of the present invention by a person of ordinaryskill in the art and the modified examples are also considered to fallwithin the scope of the present invention. For example, additions,deletions or changes in design of the constituent elements or additions,omissions, or changes in condition of the processes arbitrarilyconducted by a person of ordinary skill in the art, in the aboveembodiments, fall within the scope of the present invention as long asthey are in keeping with the spirit of the present invention.

In addition, the other advantages of the aspects described in theembodiments, which are obvious from the descriptions of the presentspecification or which can be arbitrarily conceived by a person ofordinary skill in the art, are considered to be achievable by thepresent invention as a matter of course.

What is claimed is:
 1. An illumination device comprising: a first lightguide having a first main surface, a second main surface on a sideopposite to the first main surface, a first side surface, and a secondside surface on a side opposite to the first side surface; a secondlight guide having a third main surface opposed to the second mainsurface, a fourth main surface on a side opposite to the third mainsurface, a third side surface close to the first side surface, and afourth side surface located on a side opposite to the third side surfaceand close to the second side surface; a plurality of first light sourcesopposed to the first side surface; and a plurality of second lightsources opposed to the fourth side surface, wherein the first mainsurface includes a first plane and a plurality of first grooves locatedbetween the first plane and the first side surface, the second mainsurface includes a plurality of second grooves opposed to the firstplane and orthogonal to the first grooves, and a second plane locatedbetween the second grooves and the first side surface, the third mainsurface includes a third plane and a plurality of third grooves locatedbetween the third plane and the fourth side surface and parallel to thefirst grooves, and the fourth main surface includes a plurality offourth grooves opposed to the third plane and orthogonal to the thirdgrooves, and a fourth plane located between the fourth grooves and thefourth side surface.
 2. The illumination device of claim 1, wherein thefirst side surface and the second side surface are opposed to each otherin a first direction, and the plurality of first grooves extend in thefirst direction and are arranged in a second direction orthogonal to thefirst direction.
 3. The illumination device of claim 1, wherein theplurality of first grooves are opposed to the second plane and are notopposed to the plurality of second grooves, and the plurality of thirdgrooves are opposed to the fourth plane and are not opposed to theplurality of fourth grooves.
 4. The illumination device of claim 3,wherein a boundary between the first plane and one of the first groovesoverlaps a boundary between the second plane and one of the secondgrooves, and a boundary between the third plane and one of the thirdgrooves overlaps a boundary between the fourth plane and one of thefourth grooves.
 5. The illumination device of claim 3, wherein the firstmain surface includes a fifth plane located between the plurality offirst grooves and the first side surface and opposed to the secondplane, and the third main surface includes a sixth plane located betweenthe plurality of third grooves and the fourth side surface and opposedto the fourth plane.
 6. The illumination device of claim 5, wherein theplurality of first grooves and the plurality of third grooves extend ina first direction, a length of the first grooves along the firstdirection is smaller than a length of the fifth plane along the firstdirection, and a length of the third grooves along the first directionis smaller than a length of the sixth plane along the first direction.7. The illumination device of claim 1, wherein at least part of theplurality of first grooves are opposed to the plurality of secondgrooves, and at least part of the plurality of third grooves are opposedto the plurality of fourth grooves.
 8. The illumination device of claim7, wherein the first main surface includes a fifth plane located betweenthe plurality of first grooves and the first side surface and opposed tothe second plane, and the third main surface includes a sixth planelocated between the plurality of third grooves and the fourth sidesurface and opposed to the fourth plane.
 9. The illumination device ofclaim 8, wherein a boundary between the fifth plane and one of the firstgrooves overlaps a boundary between the second plane and one of thesecond grooves, and a boundary between the sixth plane and one of thethird grooves overlaps a boundary between the fourth plane and one ofthe fourth grooves.
 10. The illumination device of claim 8, wherein aboundary between the fifth plane and one of the first grooves is opposedto the second plane, and a boundary between the sixth plane and one ofthe third grooves is opposed to the fourth plane.
 11. The illuminationdevice of claim 8, wherein the plurality of first grooves and theplurality of third grooves extend in a first direction, a length of thefirst grooves along the first direction is smaller than a length of thefifth plane along the first direction, and a length of the third groovesalong the first direction is smaller than a length of the sixth planealong the first direction.
 12. The illumination device of claim 1,wherein each of the first grooves and the third grooves is formedbetween two adjacent protruding portions, and the protruding portionshave curved surfaces.
 13. The illumination device of claim 1, whereinthe plurality of first light sources and the plurality of second lightsources are laser sources.
 14. The illumination device of claim 12,wherein a length of the first grooves along a first direction is formedaccording to the following equation (1) $\begin{matrix}{{L11} = {\frac{\tan 26.5{^\circ}}{\tan\delta}L_{0}d}} & (1)\end{matrix}$ L11: length of the first grooves along the firstdirection, δ: angle of incidence of light on the first light guide,26.5°: angle of incidence at which light is made incident on the firstlight guide at a small loss, and d: thickness of the first light guide,and a contact angle of the protruding portion is formed according to thefollowing equation (2) $\begin{matrix}{\theta = \frac{{arc}\sin\left( {\sin 2\theta_{0}\frac{\tan 26.5{^\circ}}{\tan\delta}} \right)}{2}} & (2)\end{matrix}$ θ: contact angle of the protruding portion, and Lo≥2 mmand θo≥2°.